Guide for Designing Microelectromechanical Systems in MUMPS

John C. TuckerIntroduction

The design of microelectromechanical systems can be very challenging to
the designer at times. What makes this field particularly challenging is
that the designer must have the knowledge of several different engineers
to design a working system. He/she must not only be knowledgeable with
integrated circuit layout, but also with the following,

structural engineering, such as mechanical spring design;

materials engineering, such as thin film residual stresses,

solid state engineering, such as contact resistances and parasitic, and

This is a heavy load for a designer to bear. The purpose of this guide
is to provide some guidelines for a designer with mainly IC layout experience
to design MEMS. This guide geared to the designer using the Multi­User
MEMS Processes at the MCNC. MCNC
has a guide handbook[1]
of their own that explains the process in more detail than this guide.
This guide is meant to be a starting point for the designer.

MEMS design is changing rapidly. CAD tools have risen such as the Microcosm's
MEMCAD that assist in the whole MEMS design process. Still, the design
process can be extremely iterative with each of the design aspects listed
above being improved on each process run.

Spring Design

Polysilicon springs are widely used in MEMS. There are several choices
to make when designing a polysilicon spring such as length, thickness,
shape, and number of beams. A good starting place for spring design is
with simple beam theory. A beam will deflect under force according to:

where F is the applied force, L is the beam length, E is Young's modulus
of elasticity of the material, and I is the centroid moment of inertia.
For a rectangular beam,

where x is the width and z is the thickness of the beam. If a 'T' or
'I' shaped beam is used, then the moment of inertia about the centroid
would be different. These moments of inertia can be found in a statics
book. For the derivation of these equations see Appendix A.

Combining equations 1 and 2 gives the spring constant for the beam,

where,

For structures with more than one beam the approximate spring constant
is the sum of each individual spring constant,

This is only an approximation because when beams are attached to platforms
as in Figure
4, the spring constant of each individual beam increases. This is due
to the fact that the maximum beams now have attached points on each end
and the location of maximum slope is no longer at the end of the beam.
For more details refer to Appendix
A.

Typically springs with lower spring constant are desired. To make a
spring with a lower spring constant the following can be done:

Increase the length

Decrease the thickness (This parameter is hard to change using the MUMPS
process if the bending motion is perpendicular to the substrate. The only
choices you have are between the Poly1's 2 µm or Poly2's 1.5 µm
thickness.

Add bends for torsion components and extra length

Add dimples

Actuator Design

Capacitors and springs can be used together in MEMS to make bi-stable
actuators. The force between two parallel plates of a capacitor is,

Where, A is the plate area, h is the distance between the plates, and
the V is the applied voltage. Thus, the equation for applied voltage versus
deflection can be found by combining equations [4] and [6] and rearranging,

where N is the number of support beams and K is determined by

In practice, a designer must pay attention to how field fringing will
occur when the device capacitor plates are far apart. Also, actuators are
made symmetrically (Figure
4) with at least two support beams so that the top capacitor plate
comes down parallel to the bottom. Figure
5 shows a theoretical voltage actuation curve for an actuator made
out of Poly2 with capacitor area of 6 µm by 70 µm and beams
3 µm by 70 µm.

Etching Poly Stacks

Thick structures of Poly1 and Poly2 can be fabricated with perfect alignment
between the layers by using the POLY2 mask to transfer the image on to
both layers. This is done by leaving a large sheet of Poly1 under the Poly2
and using a large POLY1_POLY2_VIA (enclosing POLY1 by 5 µm) to connect
the two. The over etch during the POLY2 image transfer etches the underlying
Poly1 layer too. Figure 6 shows this layout design. Figure 7 shows what
happens during processing. Remember, if Poly1 leads are to extend from
the structure then the POLY2 mask must extend over the POLY1_POLY2_VIA
by 5 µm so that the Poly1 leads are protected during the Poly2 etch.

Incomplete Polysilicon Etching

One common problem when patterning thick polysilicon films (especially
stacked films) is the deposition of polysilicon stringers or incomplete
etching in holes during the reactive ion etching (RIE) of the polysilicon.
As shown in Figure
8, when the separation x is to small the polysilicon is not completely
removed from the hole. Although the minimum spacing has not been thoroughly
investigated, a good rule of thumb is a minimum separation of 10 µm.

Conductive Paths

Getting electrical signals to the MEMS can be very frustrating. Any polysilicon
line can carry electrical signals to the devices. However, there paths
are very resistive. For instance, a Poly0 line 30 µm wide and 600
µm long will have a total resistance of 600 ohms (20 sqrs at 30 ohms/sqr).
Lines of Poly1 and Poly2 would of the same shape would have resistances
of 100 ohms and 200 ohms respectively. However, if the Poly2 line had only
6 µm wide metal on it the resistance would be only 6 ohms . Thus,
it is important to use metal when possible lower the path resistances.
Sometimes it is necessary to use only polysilicon lines. This occurs when
paths need to cross under or between other layers. If this is necessary
pay attention to how wide you make your paths. Obviously, the wider the
less resistive the path will be. Also, corners and contact methods can
effect the resistance of the path. For more information refer to an introductory
semiconductor fabrication text[4].

Another consideration in the electrical design is the contact resistances
between different layers. This contact resistances is mainly due to the
band alignment and mobility change at the junction of two different materials.
Table 2. shows the contact resistivities between poly layer. Metal to poly
contact resistances are currently being tested.

the Poly0 to Poly1 contact of contact area 5 µm by 5 µm
(2.5e-7cm 2) the resistance would be 122 ohms . Thus, contact
resistances can play an important role. To minimize contact resistances
make large contact areas. Of course, sometimes this sacrifices area.

Substrate Charges

Some measurement of actuator deflection versus voltage have showed that
reverse biasing the actuation voltage changes the deflection behavior.
One cause for this could be the collection of charges in the substrate
just under the nitride in figure
9. Thus, testing is being done to measure the voltage that is being
induced in the substrate due to the voltages being applied to the actuators.
Substrate contacts have also been made to set the substrate to a desired
voltage (possibly ground).

MCNC Design Rules

The following are the tables of design rules described in the "MUMPS
Design Guidelines and Rules". The purpose of these rules are to ensure
that the designer gets what he wants even with photolithography alignment
and resolution limitations. Remember that MUMPs films are very thick, wafer
surfaces are non-planar, and very thick photoresists must be used. Thus,
photolithography tolerances are very large. In other words, be conservative
and don't break the rules unless willing to take chances.

Don't over look rule R and S make lateral etch hole in large sheets
of Poly1 or Poly2 so they will have all the oxide removed from under them
during the release step. NCSU has found that 3 µm holes are sufficient
to ensure release. For double stacked poly be sure to have both HOLE1 and
HOLE2 and follow rule T. Also, if there is metal on the poly follow rule
U.

Process Variations

Process variations can play on important role in the design of a system.
For example, if an array of actuators is to be fabricated the across wafer
variation can be vary important. The cross chip variations in polysilicon
films thickness can cause extreme variations in the actuation voltages.
These effects can be extreme because the spring constants have a z3
dependence.

Polysilicon thickness standard deviations are listed at http://mems.mcnc.org/mumpst.html.
Some can be quite high while other runs have low standard deviations. For
example, one run the standard deviation for the Poly2 layer was 548 Å.
Figure
5 shows the difference between actuators with the mean Poly2 thickness
of 1.5 µm and actuators with ±548 Å thickness. Also
note that the distance between the plates can vary too when the Oxide1
and Oxide2 films vary.

Bowing of Large Polysilicon Sheets Due to Residual Stress

Large polysilicon sheets have a noticeable bowing after release due
to residual stresses. These stresses can be caused by both thermal stresses
and intrinsic stresses[2]. Thermal stress developed when two or more films
have a different coefficient of expansion. Intrinsic stresses develop when
a file is deposited at a temperature lower than its flow temperature. Thus,
a sheet of polysilicon has non-uniform residual stresses through its thickness
that causes it to curl up after release[3]. This film is said to be deposited
in compression All the polysilicon films are deposited in in tension. As
a note some other processes have films deposited in tension and these films
bend down. The residual stress is reduced after the annealing step, but
large sheets still show bending due to residual stress. As a designer,
one must simply pay attention to the fact that there are residual stresses
in films that cause them to bend after release. The residual stresses in
the MUMPS run can cause about a 4% curl up at the edges of polysilicon
beams. Thus, a beam of 100 µm length will be higher on each end by
4 µm than it is in the center. Some measures to reduce bowing are
to